TSTP Solution File: TOP004-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : TOP004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jul 23 06:26:50 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 07:17:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 GeoParameters:
% 0.19/0.44
% 0.19/0.44 tptp_input = 1
% 0.19/0.44 tptp_output = 0
% 0.19/0.44 nonempty = 1
% 0.19/0.44 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 RuleSystem INPUT:
% 0.19/0.44
% 0.19/0.44 Initial Rules:
% 0.19/0.44 #0: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_union_of_members-{F}(V1,V2), P_f1-{F}(V1,V0,V3), element_of_set-{F}(V0,V2) | element_of_set-{T}(V0,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #1: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_union_of_members-{F}(V1,V2), P_f1-{F}(V1,V0,V3), element_of_set-{F}(V0,V2) | element_of_collection-{T}(V3,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #2: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_union_of_members-{F}(V0,V2), element_of_collection-{F}(V1,V0), element_of_set-{F}(V3,V1) | element_of_set-{T}(V3,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #3: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_intersection_of_members-{F}(V0,V2), element_of_collection-{F}(V1,V0), element_of_set-{F}(V3,V2) | element_of_set-{T}(V3,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #4: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_intersection_of_members-{F}(V1,V2), P_f2-{F}(V1,V0,V3) | element_of_set-{T}(V0,V2), element_of_collection-{T}(V3,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #5: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_intersection_of_members-{F}(V1,V2), P_f2-{F}(V1,V0,V3), element_of_set-{F}(V0,V3) | element_of_set-{T}(V0,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #6: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_union_of_members-{F}(V1,V2), topological_space-{F}(V0,V1) | equal_sets-{T}(V2,V0)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #7: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V2,V1) | element_of_collection-{T}(V0,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #8: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2) | element_of_collection-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #9: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V2,V1), element_of_collection-{F}(V3,V1), P_intersection_of_sets-{F}(V4,V3,V5), element_of_collection-{F}(V4,V1) | element_of_collection-{T}(V5,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #10: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V2,V1), P_union_of_members-{F}(V3,V4), subset_collections-{F}(V3,V1) | element_of_collection-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #11: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V2), element_of_collection-{F}(V0,V1), P_f3-{F}(V3,V1,V4), P_f5-{F}(V3,V1,V5), equal_sets-{F}(V2,V3), element_of_collection-{F}(V3,V1) | topological_space-{T}(V3,V1), element_of_collection-{T}(V4,V1), subset_collections-{T}(V5,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #12: input, references = 3, size of lhs = 9:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V2), element_of_collection-{F}(V0,V1), P_f3-{F}(V3,V1,V4), P_f5-{F}(V3,V1,V5), P_union_of_members-{F}(V5,V6), equal_sets-{F}(V2,V3), element_of_collection-{F}(V3,V1), element_of_collection-{F}(V6,V1) | topological_space-{T}(V3,V1), element_of_collection-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #13: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V2), element_of_collection-{F}(V0,V1), P_f4-{F}(V3,V1,V4), P_f5-{F}(V3,V1,V5), equal_sets-{F}(V2,V3), element_of_collection-{F}(V3,V1) | topological_space-{T}(V3,V1), element_of_collection-{T}(V4,V1), subset_collections-{T}(V5,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #14: input, references = 3, size of lhs = 9:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V2), element_of_collection-{F}(V0,V1), P_f4-{F}(V3,V1,V4), P_f5-{F}(V3,V1,V5), P_union_of_members-{F}(V5,V6), equal_sets-{F}(V2,V3), element_of_collection-{F}(V3,V1), element_of_collection-{F}(V6,V1) | topological_space-{T}(V3,V1), element_of_collection-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #15: input, references = 3, size of lhs = 10:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V2), element_of_collection-{F}(V0,V1), P_f3-{F}(V3,V1,V4), P_f4-{F}(V3,V1,V5), P_intersection_of_sets-{F}(V4,V5,V6), P_f5-{F}(V3,V1,V7), equal_sets-{F}(V2,V3), element_of_collection-{F}(V3,V1), element_of_collection-{F}(V6,V1) | topological_space-{T}(V3,V1), subset_collections-{T}(V7,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #16: input, references = 3, size of lhs = 12:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V2), element_of_collection-{F}(V0,V1), P_f3-{F}(V3,V1,V4), P_f4-{F}(V3,V1,V5), P_intersection_of_sets-{F}(V4,V5,V6), P_f5-{F}(V3,V1,V7), P_union_of_members-{F}(V7,V8), equal_sets-{F}(V2,V3), element_of_collection-{F}(V3,V1), element_of_collection-{F}(V6,V1), element_of_collection-{F}(V8,V1) | topological_space-{T}(V3,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #17: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), open-{F}(V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #18: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), open-{F}(V1,V3,V2) | element_of_collection-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #19: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), element_of_collection-{F}(V3,V2) | open-{T}(V3,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #20: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), closed-{F}(V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #21: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_relative_complement_sets-{F}(V1,V2,V4), closed-{F}(V1,V2,V3) | open-{T}(V4,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #22: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), P_relative_complement_sets-{F}(V3,V1,V4), open-{F}(V4,V1,V2) | closed-{T}(V3,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #23: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), finer-{F}(V2,V3,V1) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #24: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), finer-{F}(V3,V2,V1) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #25: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), finer-{F}(V1,V2,V3) | subset_collections-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #26: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), subset_collections-{F}(V2,V1), topological_space-{F}(V3,V1), topological_space-{F}(V3,V2) | finer-{T}(V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #27: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), basis-{F}(V2,V1) | equal_sets-{T}(V3,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #28: input, references = 3, size of lhs = 8:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_collection-{F}(V2,V1), P_intersection_of_sets-{F}(V3,V2,V4), element_of_collection-{F}(V3,V1), element_of_set-{F}(V5,V4), P_f6-{F}(V6,V1,V5,V3,V2,V7), basis-{F}(V6,V1), element_of_set-{F}(V5,V6) | element_of_set-{T}(V5,V7)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #29: input, references = 3, size of lhs = 8:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_collection-{F}(V2,V1), P_intersection_of_sets-{F}(V3,V2,V4), element_of_collection-{F}(V3,V1), element_of_set-{F}(V5,V4), P_f6-{F}(V6,V1,V5,V3,V2,V7), basis-{F}(V6,V1), element_of_set-{F}(V5,V6) | element_of_collection-{T}(V7,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #30: input, references = 3, size of lhs = 8:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_collection-{F}(V2,V1), P_intersection_of_sets-{F}(V3,V2,V4), element_of_collection-{F}(V3,V1), element_of_set-{F}(V5,V4), P_f6-{F}(V6,V1,V5,V3,V2,V7), basis-{F}(V6,V1), element_of_set-{F}(V5,V6) | subset_sets-{T}(V7,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #31: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), P_f7-{F}(V2,V1,V4), equal_sets-{F}(V3,V2) | basis-{T}(V2,V1), element_of_set-{T}(V4,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #32: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), P_f8-{F}(V2,V1,V4), equal_sets-{F}(V3,V2) | basis-{T}(V2,V1), element_of_collection-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #33: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), P_f9-{F}(V2,V1,V4), equal_sets-{F}(V3,V2) | basis-{T}(V2,V1), element_of_collection-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #34: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), P_f7-{F}(V2,V1,V4), P_f8-{F}(V2,V1,V5), P_f9-{F}(V2,V1,V6), P_intersection_of_sets-{F}(V5,V6,V7), equal_sets-{F}(V3,V2) | basis-{T}(V2,V1), element_of_set-{T}(V4,V7)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #35: input, references = 3, size of lhs = 10:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), P_f7-{F}(V2,V1,V4), P_f8-{F}(V2,V1,V5), P_f9-{F}(V2,V1,V6), P_intersection_of_sets-{F}(V5,V6,V7), equal_sets-{F}(V3,V2), element_of_set-{F}(V4,V8), element_of_collection-{F}(V8,V1), subset_sets-{F}(V8,V7) | basis-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #36: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_set-{F}(V2,V1), P_top_of_basis-{F}(V3,V4), P_f10-{F}(V3,V1,V2,V5), element_of_collection-{F}(V1,V4) | element_of_set-{T}(V2,V5)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #37: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_set-{F}(V2,V1), P_top_of_basis-{F}(V3,V4), P_f10-{F}(V3,V1,V2,V5), element_of_collection-{F}(V1,V4) | element_of_collection-{T}(V5,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #38: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_set-{F}(V2,V1), P_top_of_basis-{F}(V3,V4), P_f10-{F}(V3,V1,V2,V5), element_of_collection-{F}(V1,V4) | subset_sets-{T}(V5,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #39: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_top_of_basis-{F}(V2,V3), P_f11-{F}(V2,V1,V4) | element_of_collection-{T}(V1,V3), element_of_set-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #40: input, references = 3, size of lhs = 6:
% 0.19/0.44 P_empty_set-{F}(V0), P_top_of_basis-{F}(V1,V3), element_of_collection-{F}(V2,V1), P_f11-{F}(V1,V4,V5), element_of_set-{F}(V5,V2), subset_sets-{F}(V2,V4) | element_of_collection-{T}(V4,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #41: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_subspace_topology-{F}(V1,V2,V3,V5), element_of_collection-{F}(V4,V5) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #42: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_subspace_topology-{F}(V1,V3,V2,V5), element_of_collection-{F}(V4,V5) | subset_sets-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #43: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_subspace_topology-{F}(V2,V3,V4,V5), P_f12-{F}(V2,V3,V4,V1,V6), element_of_collection-{F}(V1,V5) | element_of_collection-{T}(V6,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #44: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), P_subspace_topology-{F}(V2,V3,V4,V5), P_f12-{F}(V2,V3,V4,V1,V6), P_intersection_of_sets-{F}(V4,V6,V7), element_of_collection-{F}(V1,V5) | equal_sets-{T}(V1,V7)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #45: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_collection-{F}(V2,V1), topological_space-{F}(V3,V1), P_subspace_topology-{F}(V3,V1,V4,V5), P_intersection_of_sets-{F}(V4,V2,V6), subset_sets-{F}(V4,V3), equal_sets-{F}(V7,V6) | element_of_collection-{T}(V7,V5)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #46: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_interior-{F}(V3,V1,V2,V5), element_of_set-{F}(V4,V5) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #47: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_interior-{F}(V2,V1,V3,V5), element_of_set-{F}(V4,V5) | subset_sets-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #48: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_interior-{F}(V4,V2,V3,V5), P_f13-{F}(V4,V2,V3,V1,V6), element_of_set-{F}(V1,V5) | element_of_set-{T}(V1,V6)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #49: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_interior-{F}(V4,V2,V3,V5), P_f13-{F}(V4,V2,V3,V1,V6), element_of_set-{F}(V1,V5) | subset_sets-{T}(V6,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #50: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_interior-{F}(V4,V2,V3,V5), P_f13-{F}(V4,V2,V3,V1,V6), element_of_set-{F}(V1,V5) | open-{T}(V6,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #51: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V2,V1), subset_sets-{F}(V1,V3), P_interior-{F}(V1,V3,V4,V5), topological_space-{F}(V3,V4), open-{F}(V2,V3,V4), element_of_set-{F}(V6,V2) | element_of_set-{T}(V6,V5)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #52: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_closure-{F}(V3,V1,V2,V5), element_of_set-{F}(V4,V5) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #53: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_closure-{F}(V2,V1,V3,V5), element_of_set-{F}(V4,V5) | subset_sets-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #54: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V1,V2), P_closure-{F}(V1,V4,V3,V5), closed-{F}(V2,V4,V3), element_of_set-{F}(V6,V5) | element_of_set-{T}(V6,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #55: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V2,V1), P_closure-{F}(V2,V1,V3,V4), topological_space-{F}(V1,V3), P_f14-{F}(V2,V1,V3,V5,V6) | element_of_set-{T}(V5,V4), subset_sets-{T}(V2,V6)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #56: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V2,V1), P_closure-{F}(V2,V1,V3,V4), topological_space-{F}(V1,V3), P_f14-{F}(V2,V1,V3,V5,V6) | element_of_set-{T}(V5,V4), closed-{T}(V6,V1,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #57: input, references = 3, size of lhs = 6:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V2,V1), P_closure-{F}(V2,V1,V3,V4), topological_space-{F}(V1,V3), P_f14-{F}(V2,V1,V3,V5,V6), element_of_set-{F}(V5,V6) | element_of_set-{T}(V5,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #58: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), neighborhood-{F}(V4,V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #59: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), neighborhood-{F}(V1,V4,V2,V3) | open-{T}(V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #60: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), neighborhood-{F}(V1,V2,V4,V3) | element_of_set-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #61: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), open-{F}(V3,V1,V2), element_of_set-{F}(V4,V3) | neighborhood-{T}(V3,V4,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #62: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), limit_point-{F}(V3,V4,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #63: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), limit_point-{F}(V3,V2,V1,V4) | subset_sets-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #64: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), limit_point-{F}(V4,V3,V1,V2), P_f15-{F}(V4,V3,V1,V2,V5,V6), P_intersection_of_sets-{F}(V5,V3,V7), neighborhood-{F}(V5,V4,V1,V2) | element_of_set-{T}(V6,V7)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #65: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), limit_point-{F}(V4,V3,V1,V2), P_f15-{F}(V4,V3,V1,V2,V5,V6), neighborhood-{F}(V5,V4,V1,V2), eq_p-{F}(V6,V4) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #66: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V2,V1), topological_space-{F}(V1,V3), P_f16-{F}(V4,V2,V1,V3,V5) | limit_point-{T}(V4,V2,V1,V3), neighborhood-{T}(V5,V4,V1,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #67: input, references = 3, size of lhs = 6:
% 0.19/0.44 P_empty_set-{F}(V0), subset_sets-{F}(V2,V1), topological_space-{F}(V1,V3), P_f16-{F}(V4,V2,V1,V3,V5), P_intersection_of_sets-{F}(V5,V2,V6), element_of_set-{F}(V7,V6) | limit_point-{T}(V4,V2,V1,V3), eq_p-{T}(V7,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #68: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_boundary-{F}(V3,V1,V2,V5), element_of_set-{F}(V4,V5) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #69: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_boundary-{F}(V4,V2,V3,V5), P_closure-{F}(V4,V2,V3,V6), element_of_set-{F}(V1,V5) | element_of_set-{T}(V1,V6)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #70: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), P_boundary-{F}(V4,V2,V3,V5), P_relative_complement_sets-{F}(V4,V2,V6), P_closure-{F}(V6,V2,V3,V7), element_of_set-{F}(V1,V5) | element_of_set-{T}(V1,V7)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #71: input, references = 3, size of lhs = 8:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), P_boundary-{F}(V3,V1,V2,V5), P_closure-{F}(V3,V1,V2,V6), P_relative_complement_sets-{F}(V3,V1,V7), P_closure-{F}(V7,V1,V2,V8), element_of_set-{F}(V4,V6), element_of_set-{F}(V4,V8) | element_of_set-{T}(V4,V5)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #72: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), hausdorff-{F}(V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #73: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_set-{F}(V1,V3), element_of_set-{F}(V2,V3), P_f17-{F}(V3,V4,V1,V2,V5), hausdorff-{F}(V3,V4) | eq_p-{T}(V1,V2), neighborhood-{T}(V5,V1,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #74: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_set-{F}(V1,V3), element_of_set-{F}(V2,V3), P_f18-{F}(V3,V4,V1,V2,V5), hausdorff-{F}(V3,V4) | eq_p-{T}(V1,V2), neighborhood-{T}(V5,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #75: input, references = 3, size of lhs = 6:
% 0.19/0.44 P_empty_set-{F}(V0), element_of_set-{F}(V1,V3), element_of_set-{F}(V2,V3), P_f17-{F}(V3,V4,V1,V2,V5), P_f18-{F}(V3,V4,V1,V2,V6), hausdorff-{F}(V3,V4) | eq_p-{T}(V1,V2), disjoint_s-{T}(V5,V6)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #76: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_f19-{F}(V1,V2,V3), topological_space-{F}(V1,V2) | hausdorff-{T}(V1,V2), element_of_set-{T}(V3,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #77: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_f20-{F}(V1,V2,V3), topological_space-{F}(V1,V2) | hausdorff-{T}(V1,V2), element_of_set-{T}(V3,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #78: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), P_f19-{F}(V1,V2,V3), P_f20-{F}(V1,V2,V4), topological_space-{F}(V1,V2), eq_p-{F}(V3,V4) | hausdorff-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #79: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), P_f20-{F}(V1,V2,V3), P_f19-{F}(V1,V2,V4), topological_space-{F}(V1,V2), neighborhood-{F}(V5,V3,V1,V2), neighborhood-{F}(V6,V4,V1,V2), disjoint_s-{F}(V6,V5) | hausdorff-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #80: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), separation-{F}(V4,V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #81: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), equal_sets-{F}(V1,V0), separation-{F}(V1,V2,V4,V3) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #82: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), equal_sets-{F}(V1,V0), separation-{F}(V2,V1,V4,V3) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #83: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), separation-{F}(V2,V3,V4,V1) | element_of_collection-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #84: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), separation-{F}(V3,V2,V4,V1) | element_of_collection-{T}(V2,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #85: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_sets-{F}(V2,V3,V4), separation-{F}(V2,V3,V1,V5) | equal_sets-{T}(V4,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #86: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), separation-{F}(V1,V2,V4,V3) | disjoint_s-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #87: input, references = 3, size of lhs = 7:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_sets-{F}(V2,V1,V3), disjoint_s-{F}(V2,V1), element_of_collection-{F}(V2,V4), element_of_collection-{F}(V1,V4), topological_space-{F}(V5,V4), equal_sets-{F}(V3,V5) | equal_sets-{T}(V1,V0), equal_sets-{T}(V2,V0), separation-{T}(V2,V1,V5,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #88: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), connected_space-{F}(V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #89: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), connected_space-{F}(V1,V2), separation-{F}(V4,V3,V1,V2) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #90: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_f21-{F}(V1,V2,V3), P_f22-{F}(V1,V2,V4), topological_space-{F}(V1,V2) | connected_space-{T}(V1,V2), separation-{T}(V3,V4,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #91: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), connected_set-{F}(V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #92: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), connected_set-{F}(V1,V2,V3) | subset_sets-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #93: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_subspace_topology-{F}(V2,V3,V1,V4), connected_set-{F}(V1,V2,V3) | connected_space-{T}(V1,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #94: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), P_subspace_topology-{F}(V1,V2,V3,V4), subset_sets-{F}(V3,V1), connected_space-{F}(V3,V4) | connected_set-{T}(V3,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #95: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), open_covering-{F}(V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #96: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), open_covering-{F}(V1,V3,V2) | subset_collections-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #97: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_union_of_members-{F}(V1,V3), open_covering-{F}(V1,V2,V4) | equal_sets-{T}(V3,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #98: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), P_union_of_members-{F}(V3,V4), subset_collections-{F}(V3,V2), equal_sets-{F}(V4,V1) | open_covering-{T}(V3,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #99: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), compact_space-{F}(V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #100: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), compact_space-{F}(V1,V2), P_f23-{F}(V1,V2,V3,V4), open_covering-{F}(V3,V1,V2) | finite-{T}(V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #101: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), compact_space-{F}(V1,V2), P_f23-{F}(V1,V2,V3,V4), open_covering-{F}(V3,V1,V2) | subset_collections-{T}(V4,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #102: input, references = 3, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), compact_space-{F}(V1,V2), P_f23-{F}(V1,V2,V3,V4), open_covering-{F}(V3,V1,V2) | open_covering-{T}(V4,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #103: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_f24-{F}(V1,V2,V3), topological_space-{F}(V1,V2) | compact_space-{T}(V1,V2), open_covering-{T}(V3,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #104: input, references = 3, size of lhs = 6:
% 0.19/0.44 P_empty_set-{F}(V0), P_f24-{F}(V1,V2,V3), topological_space-{F}(V1,V2), finite-{F}(V4), subset_collections-{F}(V4,V3), open_covering-{F}(V4,V1,V2) | compact_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #105: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), compact_set-{F}(V3,V1,V2) | topological_space-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #106: input, references = 3, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), compact_set-{F}(V1,V2,V3) | subset_sets-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #107: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_subspace_topology-{F}(V2,V3,V1,V4), compact_set-{F}(V1,V2,V3) | compact_space-{T}(V1,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #108: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), topological_space-{F}(V1,V2), P_subspace_topology-{F}(V1,V2,V3,V4), subset_sets-{F}(V3,V1), compact_space-{F}(V3,V4) | compact_set-{T}(V3,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #109: input, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1), P_f-{F}(V2) | basis-{T}(V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #110: input, references = 4, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1), P_f-{F}(V2), P_top_of_basis-{F}(V2,V3), #-{F} V4 | element_of_collection-{T}(V4,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #111: input, references = 3, size of lhs = 5:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1), P_f-{F}(V2), P_top_of_basis-{F}(V2,V3), #-{F} V4 | element_of_collection-{T}(V4,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #112: input, references = 4, size of lhs = 6:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1), P_f-{F}(V2), P_top_of_basis-{F}(V2,V3), P_intersection_of_sets-{F}(V4,V5,V6), element_of_collection-{F}(V6,V3) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #113: input, references = 3, size of lhs = 1:
% 0.19/0.44 #-{F} V0 | EXISTS V1: P_union_of_members-{T}(V0,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #114: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f1-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #115: input, references = 3, size of lhs = 1:
% 0.19/0.44 #-{F} V0 | EXISTS V1: P_intersection_of_members-{T}(V0,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #116: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f2-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #117: input, references = 4, size of lhs = 0:
% 0.19/0.44 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #118: input, references = 4, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_intersection_of_sets-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #119: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f3-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #120: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f5-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #121: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f4-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #122: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_relative_complement_sets-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #123: input, references = 3, size of lhs = 5:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_f6-{T}(V0,V1,V2,V3,V4,V5)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #124: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f7-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #125: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f8-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #126: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f9-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #127: input, references = 4, size of lhs = 1:
% 0.19/0.44 #-{F} V0 | EXISTS V1: P_top_of_basis-{T}(V0,V1)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #128: input, references = 3, size of lhs = 3:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_f10-{T}(V0,V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #129: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f11-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #130: input, references = 3, size of lhs = 3:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_subspace_topology-{T}(V0,V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #131: input, references = 3, size of lhs = 4:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_f12-{T}(V0,V1,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #132: input, references = 3, size of lhs = 3:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_interior-{T}(V0,V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #133: input, references = 3, size of lhs = 4:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_f13-{T}(V0,V1,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #134: input, references = 3, size of lhs = 3:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_closure-{T}(V0,V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #135: input, references = 3, size of lhs = 4:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_f14-{T}(V0,V1,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #136: input, references = 3, size of lhs = 5:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_f15-{T}(V0,V1,V2,V3,V4,V5)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #137: input, references = 3, size of lhs = 4:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_f16-{T}(V0,V1,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #138: input, references = 3, size of lhs = 3:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_boundary-{T}(V0,V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #139: input, references = 3, size of lhs = 4:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_f17-{T}(V0,V1,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #140: input, references = 3, size of lhs = 4:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_f18-{T}(V0,V1,V2,V3,V4)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #141: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f19-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #142: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f20-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #143: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_union_of_sets-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #144: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f21-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #145: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f22-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #146: input, references = 3, size of lhs = 3:
% 0.19/0.44 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_f23-{T}(V0,V1,V2,V3)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #147: input, references = 3, size of lhs = 2:
% 0.19/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_f24-{T}(V0,V1,V2)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #148: input, references = 4, size of lhs = 0:
% 0.19/0.44 FALSE | EXISTS V0: P_cx-{T}(V0)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #149: input, references = 4, size of lhs = 0:
% 0.19/0.44 FALSE | EXISTS V0: P_f-{T}(V0)
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 number of initial rules = 150
% 0.19/0.44
% 0.19/0.44 Simplifiers:
% 0.19/0.44 #150: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_union_of_members-{F}(V0,V1), P_union_of_members-{F}(V0,V3), V1 == V3 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #151: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f1-{F}(V0,V1,V2), P_f1-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #152: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_intersection_of_members-{F}(V0,V1), P_intersection_of_members-{F}(V0,V3), V1 == V3 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #153: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f2-{F}(V0,V1,V2), P_f2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #154: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #155: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_intersection_of_sets-{F}(V0,V1,V2), P_intersection_of_sets-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #156: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f3-{F}(V0,V1,V2), P_f3-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #157: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f5-{F}(V0,V1,V2), P_f5-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #158: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f4-{F}(V0,V1,V2), P_f4-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #159: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_relative_complement_sets-{F}(V0,V1,V2), P_relative_complement_sets-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #160: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f6-{F}(V0,V1,V2,V3,V4,V5), P_f6-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #161: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f7-{F}(V0,V1,V2), P_f7-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #162: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f8-{F}(V0,V1,V2), P_f8-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #163: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f9-{F}(V0,V1,V2), P_f9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #164: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_top_of_basis-{F}(V0,V1), P_top_of_basis-{F}(V0,V3), V1 == V3 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #165: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f10-{F}(V0,V1,V2,V3), P_f10-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #166: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f11-{F}(V0,V1,V2), P_f11-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #167: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_subspace_topology-{F}(V0,V1,V2,V3), P_subspace_topology-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #168: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f12-{F}(V0,V1,V2,V3,V4), P_f12-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #169: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_interior-{F}(V0,V1,V2,V3), P_interior-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #170: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f13-{F}(V0,V1,V2,V3,V4), P_f13-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #171: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_closure-{F}(V0,V1,V2,V3), P_closure-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #172: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f14-{F}(V0,V1,V2,V3,V4), P_f14-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #173: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f15-{F}(V0,V1,V2,V3,V4,V5), P_f15-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #174: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f16-{F}(V0,V1,V2,V3,V4), P_f16-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #175: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_boundary-{F}(V0,V1,V2,V3), P_boundary-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #176: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f17-{F}(V0,V1,V2,V3,V4), P_f17-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #177: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f18-{F}(V0,V1,V2,V3,V4), P_f18-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #178: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f19-{F}(V0,V1,V2), P_f19-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #179: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f20-{F}(V0,V1,V2), P_f20-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #180: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_union_of_sets-{F}(V0,V1,V2), P_union_of_sets-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #181: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f21-{F}(V0,V1,V2), P_f21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #182: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f22-{F}(V0,V1,V2), P_f22-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #183: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f23-{F}(V0,V1,V2,V3), P_f23-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #184: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f24-{F}(V0,V1,V2), P_f24-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #185: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_cx-{F}(V0), P_cx-{F}(V1), V0 == V1 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #186: unsound, references = 3, size of lhs = 3:
% 0.19/0.44 P_f-{F}(V0), P_f-{F}(V1), V0 == V1 | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 number of simplifiers = 37
% 0.19/0.44
% 0.19/0.44 Learnt:
% 0.19/0.44 #191: mergings( V2 == V4, V3 == V5; #188 ), references = 1, size of lhs = 4:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1), P_f-{F}(V2), P_intersection_of_sets-{F}(V3,V4,V5) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #195: mergings( V3 == V5, V4 == V6; #192 ), references = 1, size of lhs = 3:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1), P_f-{F}(V2) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #199: mergings( V1 == V3, V2 == V4; #196 ), references = 1, size of lhs = 2:
% 0.19/0.44 P_empty_set-{F}(V0), P_cx-{F}(V1) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #202: mergings( V1 == V2; #200 ), references = 1, size of lhs = 1:
% 0.19/0.44 P_empty_set-{F}(V0) | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 #204: exists( #117, #200 ), references = 1, size of lhs = 0:
% 0.19/0.44 FALSE | FALSE
% 0.19/0.44 (used 0 times, uses = {})
% 0.19/0.44
% 0.19/0.44 number of learnt formulas = 5
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 randbase = 1
%------------------------------------------------------------------------------